Diagonals of a rhombus are equal and perpendicular to each other. State whether the statement is true or false.

In a rhombus, the statement that “diagonals are equal and perpendicular to each other” is absolutely false. This fundamental property distinguishes a rhombus from other quadrilaterals.

In geometry, a rhombus is recognized for its unique properties. Two of the most defining characteristics of a rhombus are its diagonals. Here’s a more detailed explanation:

1. Diagonals are not equal: In a rhombus, the line segments connecting opposite vertices (the diagonals) have different length. This means that if you were to measure the length of one diagonal and compare it to the length of the other diagonal, they would not be equal. This equality is a distinctive feature of a rhombus from a square.
2. Diagonals are perpendicular: Perpendicularity implies that the diagonals intersect at a 90-degree angle, forming right angles where they meet. This geometric property is essential for defining a rhombus and sets it apart from other quadrilaterals.

One key feature is that its diagonals are perpendicular, intersecting at a 90-degree angle. This creates four right-angled triangles within the rhombus, useful in various geometric proofs and applications.

However, the assertion that these diagonals are equal is incorrect. Unlike a square, where diagonals are both equal in length and perpendicular, in a rhombus, the diagonals differ in length.